Two line segments AC and BD bisect each other at P. Draw the diagram and prove that

(i) AB = CD

(ii) ∠BAC = ∠DCA

Prove that the median drawn from the vertex P of an isosceles triangle △PQR with PQ = PR is perpendicular to QR and bisects ∠P.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of △PQR should be equal to side AB of △ABC so that the two triangles are congruent? Give reason for your answer.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of △PQR should be equal to side BC of △ABC so that the two triangles are congruent? Give reason for your answer.